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Weighted Spectral Embedding of Graphs

Thomas Bonald, Alexandre Hollocou, Marc Lelarge
2018 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively.
more » ... e, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding. Size Top articles
doi:10.1109/allerton.2018.8636037 dblp:conf/allerton/BonaldHL18 fatcat:yvgqxnwzhzg7dhy4oqzjouxulu